[MichailZ]

Hi,

This is a question I have been stuck on for a long time... It can't be that hard, and yet I am at a complete loss as to what to do. I would be greatful if someone could do this for me:

There is a minor sector OMN of a Circle centre O and radius r. The perimeter of the sector is 100cm and the area of the sector is A cm². Given that A=50r-r² find the value of r for which A is a maximum.

If you have the C2 book, the question is C2/6D, Question 2, b, (i). Page 89.

Thanks very much,

Michail

[steve2005]

Originally Posted by MichailZ

Hi,

I hope this answers the question.

[SunGod87]

A = 50r-r^2
dA/dr = 50-2r

At a maximum dA/dr = 0
50 - 2r = 0
50 = 2r
r = 25

d^2A/dr^2 = -2

Therefore this is a maximum.

At least that's how I think you'd do it.

[MichailZ]

Thank you for your replies!

That is what I thought first, which makes A = 50r - r² = 50 x 25 - 25 x 25 = 25² = 625cm² but the answer is 120cm².

What you and me did not take into account is that 2r + rθ = Perimeter = 100.

That is what's tough...

Michail

[SunGod87]

find the value of r for which A is a maximum.

I found the value of r for when A is a maximum, post the whole question next time?

[MichailZ]

OK,

The diagram shows a minor sector OMN of a circle centre O and radius r cm. The perimeter of the sector is 100cm and the area of the sector is A cm².

(a) Show that A = 50r - r²

(b) Given that r varies, find:

(i) The value of r for which A is a maximum and show that A is a maximum

(ii) The value of Angle MON for this maximum area.

(iii) The maximum area of the sector OMN

That is the question word by word. Although there is a diagram drawn too, but it doesn't reveal much, just a sector with centre O, radius r and arc MN.

The Answers are...

2b(i) 120cm²
b(ii) 2.16
c(iii) 161.07 cm²

Thank you again for your help.

Michail

[MichailZ]

Hi,

I phoned my friend who has the solutionbank for C2, and we were right, the answer is 25. The answers in the book were wrong. Haha there's 3 hours of my life wasted on trying to get to 120cm² only to find out it was wrong...

Michail

[super_baros]

Originally Posted by MichailZ

Hi,

I phoned my friend who has the solutionbank for C2, and we were right, the answer is 25. The answers in the book were wrong. Haha there's 3 hours of my life wasted on trying to get to 120cm² only to find out it was wrong...

Michail

Yeh.... that book is always wrong... I've found some 50 + errors... just go with what seems right..... (most of the time)....

Regarding the question you are asking about.... you'll find the whole question actually done for you on page 135 in the Differentiation chapter..... hope that helps a bit more...